The key learning tasks in this lesson build on each other to support student procedural fluency, conceptual understanding, mathematical reasoning, positive dispositions toward mathematics, and the development of related academic language. Various strategies will be used to build student learning across the learning segment.
By first tapping into the students' prior knowledge of long division of integers, this will support the students in their procedural fluency of the steps involved in this process. Division of polynomials involves these same steps, which the students must gain a full understanding of and apply in order to be successful. The video shown in the beginning of class will reinforce important academic vocabulary relating to the division of polynomials, namely the mathematical terms dividend, divisor, quotient, and remainder. In addition, this video will provide them with a visual representation of the placement of these terms when setting up long division problems. This will be further reinforced by matching these terms with arrows in the first example on SmartBoard and in student presentations, as they will have to describe each term in their problem using appropriate academic language.
The inquiry-exploration activity where the students will have to determine in groups the steps involved in dividing polynomials using synthetic division by comparing it to an equivalent problem using long division will promote mathematical reasoning. This exploration will aim for the students not to be able to solve the problems solely using a strict procedure, but rather for them to gain a conceptual understanding of how the two methods relate to each other. Furthermore, by exploring these two methods, this task will help the students make better sense of how division of polynomials serves as another method of factoring, especially when working with polynomials of degree greater than two. Making connections such as these through exploration and in groups will help promote positive dispositions toward mathematics, as the students will discover relationships on their own and with their peers rather than being explicitly told all of the information concerning a given topic. When students are solely lectured and not given the chance to make their own realizations, they often turn off from learning and truly seeing the relevance of certain concepts in mathematics.
By first tapping into the students' prior knowledge of long division of integers, this will support the students in their procedural fluency of the steps involved in this process. Division of polynomials involves these same steps, which the students must gain a full understanding of and apply in order to be successful.
The video shown in the beginning of class will reinforce important academic vocabulary relating to the division of polynomials, namely the mathematical terms dividend, divisor, quotient, and remainder. In addition, this video will provide them with a visual representation of the placement of these terms when setting up long division problems. This will be further reinforced by matching these terms with arrows in the first example on SmartBoard and in student presentations, as they will have to describe each term in their problem using appropriate academic language.
The inquiry-exploration activity where the students will have to determine in groups the steps involved in dividing polynomials using synthetic division by comparing it to an equivalent problem using long division will promote mathematical reasoning. This exploration will aim for the students not to be able to solve the problems solely using a strict procedure, but rather for them to gain a conceptual understanding of how the two methods relate to each other. Furthermore, by exploring these two methods, this task will help the students make better sense of how division of polynomials serves as another method of factoring, especially when working with polynomials of degree greater than two. Making connections such as these through exploration and in groups will help promote positive dispositions toward mathematics, as the students will discover relationships on their own and with their peers rather than being explicitly told all of the information concerning a given topic. When students are solely lectured and not given the chance to make their own realizations, they often turn off from learning and truly seeing the relevance of certain concepts in mathematics.